Combinations on other puzzles

[Joel Banks]

Let's find the combinations on some of the other, less talked about puzzles. Explain how you found the combinations or probabilities on a puzzle. I'll start it off, how many combinations are on a megaminx? How many more times is this that a Rubik's cube?
(Other ideas, pyraminx, gigaminx, master pyraminx, cuboids?)

 

[Daniel Lin]

megaminx: 3^19*2^29*20!/2*30!/2=too big for my calculator
each corner can have 3 orientations and there are 20 corners. Last corner is fixed. Each edge can have 2 orientations and there are 30 edges. Last edge is fixed. There are 20!/2 ways to permute the corners and 30!/2 ways to permute edges. You divide by two because odd parity is not possible on megaminx.

 

[Joel Banks]

Awesome thanks!

 

[YouCubing]

megaminx: 3^19*2^29*20!/2*30!/2=too big for my calculator
each corner can have 3 orientations and there are 20 corners. Last corner is fixed. Each edge can have 2 orientations and there are 30 edges. Last edge is fixed. There are 20!/2 ways to permute the corners and 30!/2 ways to permute edges. You divide by two because odd parity is not possible on megaminx.

Googled it, apparently it's a little more than 10^68 a.k.a. one hundred unvigintillion.

 

[Daniel Lin]

Someone do skewb, I'm interested

 

[AlphaSheep]

You may be interested in http://www.jaapsch.net/puzzles/

You can see the number of possible combinations for more puzzles than you even thought existed.

 

[guysensei1]

I'll ask one here, how many positions are there on the Pentultimate?

Note that there are multiple orientations that one position can be in.

 

[bcube]

how many positions are there on the Pentultimate?

Third google´s result: http://www.twistypuzzles.com/~sandy/forum/viewtopic.php?f=1&t=9262&start=0

 

[gamesgamerton55]

How about gigaminx or teraminx

 

[gamesgamerton55]

How?

 

[Christopher Mowla]

How about gigaminx or teraminx

The number of positions for the minx^2 to minx^20. (minx^3=normal size, minx^5 = gigaminx, minx^7 = teraminx, etc.)

See this post for my derivation of this expression for a minx of size n (where n can be even too!).

How?

I'm not sure either why he said 6. If it's not one position, then it should be 24. (But I personally only think there is one position for the 1x1x1.)

 

[Gnome]

But I personally only think there is one position for the 1x1x1.

Agreed, 1 position (or state), 24 orientations (or external state changes that do not affect the internal state).

 

[Melvintnh327]

why does the 4x4 have 7.4 quattuordecillion possible combinations? no matter how I calculate it, I just couldn't get that number.

Edit: never mind I figured it out.

\[ \frac{8!\times3^7\times24!\times24!}{24\times4!^6}=7.4011968416\times10^{45} \]

 

[xyzzy]

quattuordecillion

Protip: avoid using the names for powers of 10 greater than 10^12, and definitely don't use them above than 10^33. "Quadrillion" (10^15) up to "decillion" (10^33) might still be understandable with some basic knowledge of Latin numbers, but it gets increasingly esoteric thereafter. (Not to mention that short scale is just completely messed up. Long scale made sense; why did we have to switch away from it…)

Anyway, yeah, your calculation is right, if you treat rotationally equivalent states as being the same. You can get the number by fixing a corner piece in place, by fixing an edge piece in place, or by dividing out the number of rotationally equivalent states (which happens to be a constant 24, because you can fix a corner piece or an edge piece). On a puzzle where every piece type has duplicates somewhere (e.g. some stickermods), it's possible that the numbers of rotationally equivalent states (the sizes of the equivalence classes, in other words) are no longer constant and you can't just divide by 24.

 

[Melvintnh327]

Protip: avoid using the names for powers of 10 greater than 10^12, and definitely don't use them above than 10^33. "Quadrillion" (10^15) up to "decillion" (10^33) might still be understandable with some basic knowledge of Latin numbers, but it gets increasingly esoteric thereafter. (Not to mention that short scale is just completely messed up. Long scale made sense; why did we have to switch away from it…)

*cough cough* I just like these names because I like math... *cough cough*
like for example: Unquadragintaquadringentillion ( \( 10^{1326} \) )

 

[abunickabhi]

*cough cough* I just like these names because I like math... *cough cough*
like for example: Unquadragintaquadringentillion ( \( 10^{1326} \) )

Thats an insanely big number. Its still much smaller than Graham's number though.

 

[Melvintnh327]

Thats an insanely big number. Its still much smaller than Graham's number though.

That number that I wrote is actually 6 times smaller than the number of possible combinations of the 19x19 rubik's cube

 

[Christopher Mowla]

That number that I wrote is actually 6 times smaller than the number of possible combinations of the 19x19 rubik's cube

No offense, but this thread is about combinations on other puzzles. So continuously bring up the nxnxn is off-topic. There are plenty of threads on the combinations of the nxnxn.

And this thread is certainly not about fascination with weird names given to large integers.

Thanks!

 

[CubeRed]

How about combinations...
On a fisher cube?

 

[Megaminx lover]

1x1x1 pyraminx?